where, \(m_{\mathrm {B}}\)  is the rest frame B-band observed peak magnitude, \(X_{1}\)  and \(\mathcal {C}\)  are time stretching of the light curve and SNe Ia color at maximum brightness respectively and \(M_{\mathrm {B}}\)  is the absolute B-band magnitude. This relation indicates that the variability of the distance modulus is governed by two additional parameters \(X_1\)  and \(\mathcal {C}\) . It must be noted here that we do have two nuisance parameters \(\alpha \)  and \(\beta \)  as well. In this paper we use the recent and largest database of SNe Ia known as the Pantheon data set. In this data set, these two nuisance parameters have been marginalized and eventually calibrated to be zero. This data set has 1048 SNe Ia measurements in the redshift range \(0.01\le z\le 2.26\)  [1]}. Hence, for the Pantheon data set, the observed distance modulus relaxes to the form \(\mu _{\mathrm {SN}}=m_{\mathrm {B}}-M_{\mathrm {B}}\) . Once we know the distance modulus, we can easily define the luminosity distance and uncertainty in observed luminosity distance as
\(d_{\mathrm {L}}^{\mathrm {obs}}(z;M_{\mathrm {B}})=10^{\left(m_{\mathrm {B}}-M_{\mathrm {B}}-25\right) / 5}(\mathrm {Mpc}), \quad \sigma _{d_{\mathrm {L}}^{obs}}=\frac{\ln (10)}{5} d_{\mathrm {L}}^{\mathrm {obs}} \sigma _{m_{\mathrm {B}}}(\mathrm {Mpc}).\) 
